Azzam al-Ahmad said last night the ceasefire was meant to ensure a “positive atmosphere,” while noting there had been “lots of progress” in the talks.
A Hamas official earlier said the truce had been extended for 72 hours.
Israeli officials declined to comment.
The Israeli military said at least three rockets have been fired at Israel despite Hamas saying the ceasefire is extended.
Earlier, Israeli police said a rocket landed in Israel two hours before the end of the truce. It fell in an open area and caused no damage or injuries, a spokeswoman said.
Hamas denied responsibility for the rocket attack.
Egyptian mediators had been racing to pin down a long-term ceasefire between Israel and Hamas to prevent more fighting in the Gaza war when the earlier truce had been set to expire at 12 midnight.
During the temporary truce, Israel halted military operations in the war-battered coastal territory and Gaza militants stopped firing rockets.
“We have finished talks today without agreement. More work needs to be done to have a better deal,” a Hamas official said earlier yesterday. “We are deliberating internally over an offer to extend the ceasefire.”
A ceasefire extension would grant both sides additional time to negotiate a more sustainable truce and a roadmap for Gaza.
Hamas is seeking an end to a crippling blockade imposed by Israel and Egypt in 2007. The blockade has greatly limited the movement of Palestinians in and out of the territory of 1.8 million people. It also restricted the flow of goods into Gaza and blocked virtually all exports.
Israel wants Hamas to disarm, or at least be prevented from re-arming. Hamas has recovered from previous rounds of violence with Israel, including a three-week ground operation in January 2009 and another week-long air offensive in 2012.
Gaza militants fired over 3,000 rockets toward Israel during the war.
As the talks continued, Hamas indicated it was sticking to its demands. In remarks broadcast yesterday, Ismail Haniyeh, the top Hamas leader in Gaza, said that “achieving a permanent truce can come only through lifting the blockade on Gaza”.